Hi, I have a few basic doubts in the QPSK modulation & drawing of constellation, 1) For the QPSK modulation complex signal is required (or) real signal is enough? 2) In the drawing of constellation x-axis is the real value ,y-axis is imaginary & how the angle is represented in the constellation? 3) If the QPSK signal is the complex signal,which formula will suits for the representation of 1 st quadrant symbol cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t + (pi/4)) (or) cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t - (pi/4)) Please explain these basic questions Thanking u in advance Regards, KIRAN KUMAR
Few basic doubts in the QPSK modulation & drawing of constellation
Started by ●November 26, 2010
Reply by ●November 26, 20102010-11-26
>Hi, > >I have a few basic doubts in the QPSK modulation & drawing of >constellation, > >1) For the QPSK modulation complex signal is required (or) real signal is >enough? >Ans: Complex>2) In the drawing of constellation x-axis is the real value ,y-axis is >imaginary & how the angle is represented in the constellation? >Ans: 45 Deg>3) If the QPSK signal is the complex signal,which formula will suits for >the representation of 1 st quadrant symbol > >cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t + (pi/4)) > >(or) > >cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t - (pi/4)) >Ans: http://en.wikipedia.org/wiki/Phase-shift_keying
Reply by ●November 26, 20102010-11-26
On 11/26/2010 07:43 AM, kiran2urs wrote:> Hi, > > I have a few basic doubts in the QPSK modulation& drawing of > constellation, > > 1) For the QPSK modulation complex signal is required (or) real signal is > enough?There seems to be a lot of confusion on this subject lately. Radio signals are entirely real -- there are no imaginary numbers in this real world of ours*. Imaginary numbers are handy for radio applications. They're handy because they are an exact mathematical stand-in for representing radio signals in quadrature, even going so far as to have formal mathematical ties to the Fourier transform. So if you have a (real) radio signal x(t) = a(t) * cos(w * t) + b(t) * sin(w * t), then you can _represent_ it as x_m(t) = a(t) + i * b(t) (where i = sqrt(-1)), and say that x(t) = (x_m(t) * e^(i * w * t) + (x_m(t))' * e^(-i * w * t))/2, where (x_m(t))' is the complex conjugate of x_m(t). Furthermore, you can perform a quadrature downconversion on x(t) that gives you two channels that _act_ like a real and an imaginary part, and upon which you can perform arithmetic that is _behaviorally_ exactly _like_ complex arithmetic. I emphasize the words "represent", "act", "behaviorally" and "like" because your never, ever actually have imaginary quantities floating around -- this is the real world. Even inside a computer algorithm, all numbers are real. We can only simulate complex arithmetic, and in this case keep in mind that we're doing _quadrature_ arithmetic, which is like complex arithmetic in all the details, but is still different.> 2) In the drawing of constellation x-axis is the real value ,y-axis is > imaginaryThat is the typical way of doing it, yes.> & how the angle is represented in the constellation?I'm not sure what you mean. Angle is angle.> 3) If the QPSK signal is the complex signal,which formula will suits for > the representation of 1 st quadrant symbol > > cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t + (pi/4)) > > (or) > > cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t - (pi/4))Neither. In complex representation a signal that's centered in the 1st quadrant would be something like 1 + i. In real radio terms this would be cos(w * t) + sin(w * t). -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html